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Estimation of the Basic Reproductive Ratio for Dengue Fever at the Take-Off Period of Dengue Infection.

- Comput Math Methods Med (2015)

Bottom Line: The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans.Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa.We conclude that the second approach is more realistic, compared with our first approach and the previous work.

View Article: PubMed Central - PubMed

Affiliation: Departemen Matematika, FMIPA, Institut Teknologi Bandung, Bandung, Indonesia ; Jurusan Matematika, FST, Universitas Nusa Cendana, Kupang, Indonesia.

ABSTRACT
Estimating the basic reproductive ratio ℛ 0 of dengue fever has continued to be an ever-increasing challenge among epidemiologists. In this paper we propose two different constructions to estimate ℛ 0 which is derived from a dynamical system of host-vector dengue transmission model. The construction is based on the original assumption that in the early states of an epidemic the infected human compartment increases exponentially at the same rate as the infected mosquito compartment (previous work). In the first proposed construction, we modify previous works by assuming that the rates of infection for mosquito and human compartments might be different. In the second construction, we add an improvement by including more realistic conditions in which the dynamics of an infected human compartments are intervened by the dynamics of an infected mosquito compartment, and vice versa. We apply our construction to the real dengue epidemic data from SB Hospital, Bandung, Indonesia, during the period of outbreak Nov. 25, 2008-Dec. 2012. We also propose two scenarios to determine the take-off rate of infection at the beginning of a dengue epidemic for construction of the estimates of ℛ 0: scenario I from equation of new cases of dengue with respect to time (daily) and scenario II from equation of new cases of dengue with respect to cumulative number of new cases of dengue. The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans. Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa. We conclude that the second approach is more realistic, compared with our first approach and the previous work.

No MeSH data available.


Related in: MedlinePlus

The ratio of ℛ0A/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of the infected mosquito per human index ρ for λ from the second scenario.
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fig14: The ratio of ℛ0A/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of the infected mosquito per human index ρ for λ from the second scenario.

Mentions: From Figures 7–14, not only do we obtain the value of the basic reproductive ratio estimation of the ℛ0A which is greater than one but also we do obtain the value which is less than one; for instance, from the first scenario at λ = 0.190 and ρ = 0.67 we have ℛ0A = 0.67 < 1 (see Table 7). Also, we can determine the intersection range of a basic reproductive ratio from a different construction of value of λ. Both proposed constructions of ℛ0 are the same when using assumption in [12] for these particular cases. But increasing the number of secondary cases for every t.o.p. will depend on k for the first construction and depend on ρ for the second construction. These results indicate that the greater the number of mosquitoes means the higher the number of new cases of dengue and the shorter the period of the i.t.o.p. of dengue infection. Furthermore, ℛ0F estimates of ℛ0 are too low when compared to ℛ0A. This is very dangerous in application, since the intervention to control dengue that results from ℛ0F estimation will not be able to stop the disease once it exists. Therefore, prevention of dengue incidences is more appropriate if it is done early, and exactly how early is dependent on ℛ0A estimation.


Estimation of the Basic Reproductive Ratio for Dengue Fever at the Take-Off Period of Dengue Infection.

- Comput Math Methods Med (2015)

The ratio of ℛ0A/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of the infected mosquito per human index ρ for λ from the second scenario.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4561940&req=5

fig14: The ratio of ℛ0A/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of the infected mosquito per human index ρ for λ from the second scenario.
Mentions: From Figures 7–14, not only do we obtain the value of the basic reproductive ratio estimation of the ℛ0A which is greater than one but also we do obtain the value which is less than one; for instance, from the first scenario at λ = 0.190 and ρ = 0.67 we have ℛ0A = 0.67 < 1 (see Table 7). Also, we can determine the intersection range of a basic reproductive ratio from a different construction of value of λ. Both proposed constructions of ℛ0 are the same when using assumption in [12] for these particular cases. But increasing the number of secondary cases for every t.o.p. will depend on k for the first construction and depend on ρ for the second construction. These results indicate that the greater the number of mosquitoes means the higher the number of new cases of dengue and the shorter the period of the i.t.o.p. of dengue infection. Furthermore, ℛ0F estimates of ℛ0 are too low when compared to ℛ0A. This is very dangerous in application, since the intervention to control dengue that results from ℛ0F estimation will not be able to stop the disease once it exists. Therefore, prevention of dengue incidences is more appropriate if it is done early, and exactly how early is dependent on ℛ0A estimation.

Bottom Line: The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans.Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa.We conclude that the second approach is more realistic, compared with our first approach and the previous work.

View Article: PubMed Central - PubMed

Affiliation: Departemen Matematika, FMIPA, Institut Teknologi Bandung, Bandung, Indonesia ; Jurusan Matematika, FST, Universitas Nusa Cendana, Kupang, Indonesia.

ABSTRACT
Estimating the basic reproductive ratio ℛ 0 of dengue fever has continued to be an ever-increasing challenge among epidemiologists. In this paper we propose two different constructions to estimate ℛ 0 which is derived from a dynamical system of host-vector dengue transmission model. The construction is based on the original assumption that in the early states of an epidemic the infected human compartment increases exponentially at the same rate as the infected mosquito compartment (previous work). In the first proposed construction, we modify previous works by assuming that the rates of infection for mosquito and human compartments might be different. In the second construction, we add an improvement by including more realistic conditions in which the dynamics of an infected human compartments are intervened by the dynamics of an infected mosquito compartment, and vice versa. We apply our construction to the real dengue epidemic data from SB Hospital, Bandung, Indonesia, during the period of outbreak Nov. 25, 2008-Dec. 2012. We also propose two scenarios to determine the take-off rate of infection at the beginning of a dengue epidemic for construction of the estimates of ℛ 0: scenario I from equation of new cases of dengue with respect to time (daily) and scenario II from equation of new cases of dengue with respect to cumulative number of new cases of dengue. The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans. Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa. We conclude that the second approach is more realistic, compared with our first approach and the previous work.

No MeSH data available.


Related in: MedlinePlus